Short answer:
Raster images use dots in a grid to make a picture. Vector images use a list of geometric shapes.

Long answer:
Raster graphics use a 2-dimensional array grid array of "pixels", or dots. Each pixel carries its own information about color, hue, etc. A typical raster image can store compressed information about more than a million of these individual pixels, packed in a square or rectangular area. When seen from a distance, this grid of pixels appears to the human eye to present an image. Some formats like GIF even include a way to store multiple overlapping grids which, when shown sequentially, can produce a sprite or animation. There is no math data in raster graphics, only a collection of "dumb" pixels with color, which makes it an ideal format for photos etc.

Vector graphics use a predefined set of real math-based "entities", or shape objects, that define geometry such as circles, lines, splines, etc. Additional characteristics of each entity such as color and lineweight may also be included. Simple entities can be collected to represent complex ones, such as two circles and some line entities into a single 3D cylinder entity. This makes vector graphics ideal for CAD and CAM.

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